Question:
A body has a weight 90 kg on the earths surface, the mass of the moon is 1/9 that of the earths mass and its radius is 1/2 that of the earths radius. On the moon the weight of the body is:
A body has a weight 90 kg on the earths surface, the mass of the moon is 1/9 that of the earths mass and its radius is 1/2 that of the earths radius. On the moon the weight of the body is:
Updated On: May 12, 2024
- 45 kg
- 202.5 kg
- 90 kg
- 40 kg
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The Correct Option is D
Solution and Explanation
Acceleration due to gravity on earth is given by $ \frac{m{{\upsilon }^{2}}}{r}=4mg $ $ \therefore $ Hence $ {{\upsilon }^{2}}=4rg $ $ \upsilon =\sqrt{4rg} $ or $ \upsilon =\sqrt{4\times 2.5\times 9.8} $ $ \upsilon =\sqrt{98}\,\,m/s $ Weight of body on moon $ \text{2}0\text{ g }=\text{ 2}\times \text{1}{{0}^{-\text{2}}}\text{ kg}, $ $ =\frac{360\times 5}{18}=100m/s $
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Concepts Used:
Escape Speed
Escape speed is the minimum speed, which is required by the object to escape from the gravitational influence of a plannet. Escape speed for Earth’s surface is 11,186 m/sec.
The formula for escape speed is given below:
ve = (2GM / r)1/2
where ,
ve = Escape Velocity
G = Universal Gravitational Constant
M = Mass of the body to be escaped from
r = Distance from the centre of the mass